cp's OEIS Frontend

A337586 Triangle read by rows: T(n, k) is the number of integer multisets of size k (partitions of k) for which the number of partitions of n with matching multiplicity multiset is odd (n >= 1, 1 <= k <= n).

%I A337586 #12 Nov 23 2020 13:02:27
%S A337586 1,1,1,1,1,1,1,2,1,1,1,0,0,1,1,1,1,3,2,1,1,1,1,2,1,2,1,1,1,2,1,3,3,2,
%T A337586 1,1,1,0,3,0,3,3,2,1,1,1,1,0,3,3,3,3,2,1,1,1,1,2,3,2,1,5,3,2,1,1,1,2,
%U A337586 2,1,3,7,3,5,3,2,1,1,1,0,0,2,2,2,5,3,5,3,2,1,1,1,1,0,3,3,4,5,5,3,5,3
%N A337586 Triangle read by rows: T(n, k) is the number of integer multisets of size k (partitions of k) for which the number of partitions of n with matching multiplicity multiset is odd (n >= 1, 1 <= k <= n).
%C A337586 The relevant partitions of n have exactly k parts.
%C A337586 The number of multiplicity multisets of size k met by a positive even number of partitions of n is A337584(n, k) - T(n, k).
%H A337586 Álvar Ibeas, <a href="/A337586/b337586.txt">First 72 rows, flattened</a>
%H A337586 Álvar Ibeas, <a href="/A337586/a337586.txt">First 30 rows</a>
%F A337586 T(n, k) == A008284(n, k) (mod 2).
%F A337586 If k > (2*n+1)/3, T(n, k) = A337585(n - k).
%e A337586 The 3 = A008284(6, 2) partitions of 6 into 2 parts show 2 = A337584(6, 2) different multiplicity multisets: (1, 1) is attained by two of those partitions ((5, 1) and (4, 2)) and the other (2) just by one, (3, 3). Then, T(6, 2) = 1.
%e A337586 Triangle begins:
%e A337586   k:  1 2 3 4 5 6 7 8 9 10
%e A337586       --------------------
%e A337586 n=1:  1
%e A337586 n=2:  1 1
%e A337586 n=3:  1 1 1
%e A337586 n=4:  1 2 1 1
%e A337586 n=5:  1 0 0 1 1
%e A337586 n=6:  1 1 3 2 1 1
%e A337586 n=7:  1 1 2 1 2 1 1
%e A337586 n=8:  1 2 1 3 3 2 1 1
%e A337586 n=9:  1 0 3 0 3 3 2 1 1
%e A337586 n=10: 1 1 0 3 3 3 3 2 1 1
%Y A337586 Cf. A008284, A337585 (row sums), A337584.
%K A337586 nonn,tabl
%O A337586 1,8
%A A337586 _Álvar Ibeas_, Sep 02 2020